C. When you add two integers, does the order of the numbers make a difference? Illustrate your answer by showing each of these pairs of sums on a number line. 1. –5 + (+10) and +10 + -5
→→→→→→→→→→→→→
←←←←←←←
-6-5-4 -3-2-10123 4567 89 10
1. You can think of the scoring in MathMania as follows: When a team answers a question correctly, a positive integer is added to their score. When a team answers a question incorrectly, a negative integer is added to their score. For each of the following situations, write an addition sentence that will give the team’s score. Assume each team starts with 0 points. a. The Brainiacs answer a 200-point question correctly and a 150-point question incorrectly. 0 + 200 + -150 = +50
b. The Aliens answer a 100-point question correctly and a 100-point question incorrectly. 0 + 100 + -100 = 0
c. The Prodigies answer a 50-point question incorrectly, a 100-point question incorrectly, and a 250-point question correctly. 0 + -50 + -100 + (+250) = +100
2. Illustrate each addition problem on a number line and give the answer. a. –2 + (+2) = 0
→→→
←←←
-5-4-3-2 -10 1 2 3 4 5
3. What happens when you add opposites? Explain how you know your answer is correct. When you add opposites the answer will always be zero, because you’re adding the same values from opposite sides. So if you have the problem, +2 + -2, it equals 0, because you have 2, but then you add –2, leaving you with 0. You have a value, but then you add or take away that same value, which always leaves you with zero.
Eva v. V.
Big Idea: Negative numbers help us to model many real world situations
Essential Question: How can I add integers?
2.1 Adding on a Number Line
A. Write the addition sentence illustrated by each figure.
1.
←←←←←
←←←
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-3 + -4 = -7
2. →→→→→
←←←←
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-3 + (+4) = +1
3.
→→→→→→→→→→→→→→
←←←←←←
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-4 + (+11) = +7
4. ←←←←←←←←←
→→→→→
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
+5 + -8 = -3
B. Illustrate each addition problem on a number line, and give the answer.
1. –5 + (+8) = +3
→→→→→→→→→→
←←←←←←←
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
2. –4 + -3 = -7
←←←←←
←←←←←←
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
3. –2 + -3 + (+10) = +5
→→→→→→→→→→→→→
←←←←←
←←←
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
C. When you add two integers, does the order of the numbers make a difference? Illustrate your answer by showing each of these pairs of sums on a number line.
1. –5 + (+10) and +10 + -5
→→→→→→→→→→→→→
←←←←←←←
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
←←←←←←
→→→→→→→→→→→→
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
2. –4 + -6 and –6 + -4
←←←←←←←←←
←←←←←←
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
←←←←←←
←←←←←←←←←
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
3. +8 + -8 and –8 + (+8)
←←←←←←←←←
→→→→→→→→→
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
→→→→→→→→→→→→
←←←←←←←←←←←←
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
4. +6 + -7 and –7 + (+6)
←←←←←←←←
→→→→→→→
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
→→→→→→→→→
←←←←←←←←←←
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
Follow – Up
1. You can think of the scoring in MathMania as follows: When a team answers a question correctly, a positive integer is added to their score. When a team answers a question incorrectly, a negative integer is added to their score. For each of the following situations, write an addition sentence that will give the team’s score. Assume each team starts with 0 points.
a. The Brainiacs answer a 200-point question correctly and a 150-point question incorrectly.
0 + 200 + -150 = +50
b. The Aliens answer a 100-point question correctly and a 100-point question incorrectly.
0 + 100 + -100 = 0
c. The Prodigies answer a 50-point question incorrectly, a 100-point question incorrectly, and a 250-point question correctly.
0 + -50 + -100 + (+250) = +100
2. Illustrate each addition problem on a number line and give the answer.
a. –2 + (+2) = 0
→→→
←←←
-5 -4 -3 -2 -1 0 1 2 3 4 5
b. +8 + -8 = 0
←←←←←←←←←
→→→→→→→→→
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
c. –1 + (+1) = 0
→
←
-3 -2 -1 0 1 2 3
3. What happens when you add opposites? Explain how you know your answer is correct.
When you add opposites the answer will always be zero, because you’re adding the same values from opposite sides. So if you have the problem, +2 + -2, it equals 0, because you have 2, but then you add –2, leaving you with 0. You have a value, but then you add or take away that same value, which always leaves you with zero.